Q. Energy and radius of first Bohr orbit of He$^+$ and Li$^{2+}$ are [Given $R_H = 2.18\times10^{-18}$ J, $a_0 = 52.9$ pm]
A) $E_n(Li^{2+}) = -19.62 \times 10^{-18}$ J: $r_n(Li^{2+}) = 17.6$ pm $E_n(He^+) = -8.72\times10^{-18}$ J; $r_n(He^+) = 26.4$ pm
B) $E_n(Li^{2+}) = -8.72 \times 10^{-18}$ J; $r_n(Li^{2+}) = 26.4$ pm $E_n(He^+) = -19.62 \times 10^{-18}$ J: $r_n(He^+) = 17.6$ pm
C) $E_n(Li^{2+}) = -19.62 \times 10^{-16}$ J; $r_n(Li^{2+}) = 17.6$ pm $E_n(He^+) = -8.72 \times 10^{-16}$ J: $r_n(He^+) = 26.4$ pm
D) $E_n(Li^{2+}) = -8.72 \times 10^{-16}$ J; $r_n(Li^{2+}) = 17.6$ pm $E_n(He^{2+}) = -19.62 \times 10^{-16}$ J: $r_n(He^+) = 17.6$ pm
Explanation
[Solution by Claude - not from source] $E_1=-R_HZ^2$: $Li^{2+}$ ($Z=3$) $=-19.62\times10^{-18}$ J; $He^+$ ($Z=2$) $=-8.72\times10^{-18}$ J. $r=a_0/Z$: $Li^{2+}$ $=17.6$ pm; $He^+$ $=26.4$ pm. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.